A Fast Algorithm Based on a Sylvester-like Equation for LS Regression with GMRF Prior
This provides an incremental improvement for researchers in multichannel image processing by speeding up regression computations.
The paper tackles penalized least squares regression with a 2D Gaussian Markov random field prior by formulating it as a Sylvester-like matrix equation and solving it analytically, leading to a fast algorithm that can be integrated into proximal methods.
This paper presents a fast approach for penalized least squares (LS) regression problems using a 2D Gaussian Markov random field (GMRF) prior. More precisely, the computation of the proximity operator of the LS criterion regularized by different GMRF potentials is formulated as solving a Sylvester-like matrix equation. By exploiting the structural properties of GMRFs, this matrix equation is solved columnwise in an analytical way. The proposed algorithm can be embedded into a wide range of proximal algorithms to solve LS regression problems including a convex penalty. Experiments carried out in the case of a constrained LS regression problem arising in a multichannel image processing application, provide evidence that an alternating direction method of multipliers performs quite efficiently in this context.